Richtmyer -- Meshkov instability in reactive mixtures

This research analyzes the effect of reactivity on the Richtmyer-Meshkov instability with particular emphasis on the velocity and wave number scaling and on the effect of free detonation instability modes on the interface corrugation rate. This analysis is performed by solving numerically for the first order perturbation generated by the shock-induced acceleration of an initially corrugated interface.;The objective of this research is to analyze the effect of mixture reactivity on the process supported by a shock sweeping across a corrugated interface from high density to low density fluid. This scenario is antithetical to the classical Richtmyer analysis where transmitted and reflected shock waves are generated by shock transit from low to high density mixture. A linear stability analysis of the Richtmyer-Meshkov instability supporting the detonation initiation is presented. The analysis focuses on scaling of the interface growth rate with the perturbation wave number under combustion conditions, and on the coupling between detonation front and interface instabilities. This research documents the method, numerical convergence of the solution, and results obtained assuming finite rate kinetics. The results show a profound effect of the reactivity on both the short time growth and the long time linear regime.